That is not how Broadcom routers work. They have a CFE, which is equivalent to a BIOS (it's just their version of U-Boot or RedBoot), and the firmware available for download is equivalent to an OS. The better manufacturers actually put the CFE on a separate NOR serial chip rather than on the NAND flash along with the firmware, so it's way harder to corrupt.
I seriously do not understand why no router manufacturer using Broadcom SoC except ASUS leaves the recovery webserver enabled in the CFE--as it is supplied to them by Broadcom, if the firmware fails to boot or you press the reset button right after power-on it will take you to a webpage where you can do nothing except upload firmware. Most companies intentionally disable that for some reason, but some like Netgear will at least leave the TFTP running so if you time it just right you can begin uploading a firmware before the firmware boots.
TP-Link disables both the recovery webserver and TFTP so your only option is to open it up, attach a USB to TTL Serial adapter and hit CTRL-C to stop the boot process, then via commandline enable the TFTP option. To add insult to injury, TP-Link usually does not put pins into the serial header so soldering is required--hey something has to give if you are cheapest. I think they want it to break and be so inconvenient to fix that you will buy a new one.
Since it is boot cycling over and over, either you have a bad PSU (which is very common), or the firmware is good enough to start booting but then crashes after the CFE hands off control to it.
There is no known 3rd party firmware for that router, but hardware-wise it is very similar to the Archer C3150 or RT-AC88U/RT-AC3100 or DIR-885L. It's probably closest to the latter because that one also features two flash chips, but if you wanted 3rd party firmware support it's worth paying more for a more popular router.